need help solving this

Question

Find all the real zeros of the polynomial. Use the quadratic formula if necessary. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

P(x) = 2x3 + 8x2 + 6x − 4

Answer 1

A minor solution strategy:

2x³ +8x² + 6x -4 = 0

Since we can factor out 2, and divide both sides by 2, the solution set of the above equation is identical to that of:

x³ + 4x² + 3x -2 = 0

This makes applying the rational root theorem somewhat simpler:

±{1, 2} is the entire set of potential rational solutions.

With the original equation, the entire set of potential rational solutions would be:

±{1, 2, 1/2, 4}.

In essence, we cut our solution search in half.

And -2 turns out to be a solution, so we can factor that out and reduce a cubic equation to a quadratic one. Applying the quadratic formula provides us with a pair of irrational "conjugate" roots.

And that is all three roots of this cubic equation.

Answer 2

-2, -1 - √2, -1 + √2